scholarly journals Decay-rate power-law exponent as a link between dissociation energy and temperature

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Paul Fischer ◽  
Lutz Schweikhard
Keyword(s):  
Decay Rate ◽  
Power Law ◽  
Dissociation Energy ◽  
Power Law Exponent

Regional variation of recession flow power-law exponent

2018 ◽  
Vol 32 (7) ◽  
pp. 866-872 ◽  
Author(s):  
Swagat Patnaik ◽  
Basudev Biswal ◽  
Dasika Nagesh Kumar ◽  
Bellie Sivakumar
Keyword(s):  
Power Law ◽  
Regional Variation ◽  
Power Law Exponent ◽  
Flow Power

scholarly journals Growth Rate Exponents of Richtmyer-Meshkov Mixing Layers

2005 ◽  
Vol 73 (3) ◽  
pp. 461-468 ◽  
Author(s):  
Timothy T. Clark ◽  
Ye Zhou
Keyword(s):  
Flow Field ◽  
Power Law ◽  
Mixing Layer ◽  
Power Laws ◽  
Mixing Layers ◽  
Spatial Gradients ◽  
Power Law Exponent ◽  
Virtual Time ◽  
Time Origin ◽  
Density Ratios

The Richtmyer-Meshkov mixing layer is initiated by the passing of a shock over an interface between fluid of differing densities. The energy deposited during the shock passage undergoes a relaxation process during which the fluctuational energy in the flow field decays and the spatial gradients of the flow field decrease in time. This late stage of Richtmyer-Meshkov mixing layers is studied from the viewpoint of self-similarity. Analogies with weakly anisotropic turbulence suggest that both the bubble-side and spike-side widths of the mixing layer should evolve as power-laws in time, with the same power-law exponent and virtual time origin for both sides. The analogy also bounds the power-law exponent between 2∕7 and 1∕2. It is then shown that the assumption of identical power-law exponents for bubbles and spikes yields fits that are in good agreement with experiment at modest density ratios.

scholarly journals Free Convective MHD Flow Past a Vertical Cone with Variable Heat and Mass Flux

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
J. Prakash ◽  
S. Gouse Mohiddin ◽  
S. Vijaya Kumar Varma
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Mass Flux ◽  
Numerical Study ◽  
Convection Boundary Layer ◽  
Vertical Cone ◽  
Local Skin ◽  
Surface Mass ◽  
Flow Past ◽  
Power Law Exponent

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to qwx=xm and qw*(x)=xm, respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

scholarly journals Differences in power-law growth over time and indicators of COVID-19 pandemic progression worldwide

2020 ◽  
Author(s):  
Jack Merrin
Keyword(s):  
Error Analysis ◽  
Real Time ◽  
Power Law ◽  
Growth Phase ◽  
Exponential Growth ◽  
Spreading Rate ◽  
Exponential Growth Phase ◽  
Power Law Exponent ◽  
Disease Spreading ◽  
Over Time

1AbstractAn automated statistical and error analysis of 45 countries or regions with more than 1000 cases of COVID-19 as of March 28, 2020, has been performed. This study reveals differences in the rate of disease spreading rate over time in different countries. This survey observes that most countries undergo a beginning exponential growth phase, which transitions into a power-law phase, as recently suggested by Ziff and Ziff. Tracking indicators of growth, such as the power-law exponent, are a good indication of the relative danger different countries are in and show when social measures are effective towards slowing the spread. The data compiled here are usefully synthesizing a global picture, identifying country to country variation in spreading, and identifying countries most at risk. This analysis may factor into how best to track the effectiveness of social distancing policies and quarantines in real-time as data is updated each day.

scholarly journals Scale-free networks with the power-law exponent between 1 and 3

2007 ◽  
Vol 56 (10) ◽  
pp. 5635
Author(s):  
Guo Jin-Li ◽  
Wang Li-Na
Keyword(s):  
Power Law ◽  
Scale Free ◽  
Power Law Exponent ◽  
Scale Free Networks

scholarly journals Typical Distances in Ultrasmall Random Networks

2012 ◽  
Vol 44 (2) ◽  
pp. 583-601 ◽  
Author(s):  
Steffen Dereich ◽  
Christian Mönch ◽  
Peter Mörters
Keyword(s):  
Power Law ◽  
Preferential Attachment ◽  
Shortest Paths ◽  
Giant Component ◽  
Configuration Model ◽  
Random Networks ◽  
Power Law Exponent ◽  
Extra Factor ◽  
Typical Distances

We show that in preferential attachment models with power-law exponent τ ∈ (2, 3) the distance between randomly chosen vertices in the giant component is asymptotically equal to (4 + o(1))log log N / (-log(τ − 2)), where N denotes the number of nodes. This is twice the value obtained for the configuration model with the same power-law exponent. The extra factor reveals the different structure of typical shortest paths in preferential attachment graphs.

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